Bayesian inference and prediction in single server M/M/1 queuing model based on queue length

• Published in: Communications in statistics. Simulation and computation Vol. 50; no. 6; pp. 1576 - 1588
• Main Authors: Basak, Arpita, Choudhury, Amit
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 05.07.2021; Taylor & Francis Ltd
• Subjects: Bayes factor; Bayesian analysis; Bayesian estimation; M/M/1 queue; Maximum likelihood estimators; Predictive distribution; Queues; Statistical inference
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2019.1586924

This paper is concerned with the problem of estimating traffic intensity, ρ for single server queuing model in which inter-arrival and service times are exponentially distributed (Markovian) using data on queue size (number of customers present in the queue) observed at any random point of time. Here, it is assumed that q is unknown but random quantity. Bayes estimator of ρ are derived under squared error loss function assuming two forms of prior information on ρ. The performance of the proposed Bayes estimators is compared with that of the corresponding classical version estimator based on maximum likelihood principle. The model comparison criterion based on Bayes factor is used to select a suitable prior for Bayesian analysis.